{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#!pip3 install python-mnist\n",
    "#!pip3 install sklearn\n",
    "#!pip3 install matplotlib\n",
    "\n",
    "import sklearn\n",
    "from sklearn import metrics\n",
    "from sklearn.utils import shuffle\n",
    "from sklearn.neural_network import MLPClassifier\n",
    "from sklearn import preprocessing\n",
    "from mnist.loader import MNIST\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import copy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Load MNIST dataset from file #\n",
    "It will be normalized using the sklearn.preprocessing.Normalizer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "mndata = MNIST('dataset')\n",
    "\n",
    "tr_images, tr_labels = mndata.load_training()\n",
    "ts_images, ts_labels = mndata.load_testing()\n",
    "\n",
    "preproc = preprocessing.Normalizer()\n",
    "\n",
    "tr_images = np.array(preproc.fit_transform(tr_images))\n",
    "ts_images = np.array(preproc.transform(ts_images))\n",
    "\n",
    "tr_labels = np.array(tr_labels)\n",
    "ts_labels = np.array(ts_labels)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Save to file (as an image) a slice of data #\n",
    "(Create manually the \"images\" directory if not present)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def print_img(data, filename, epoch=\"\"):\n",
    "    size_img = int(np.sqrt(data.shape[1]))\n",
    "    X = np.rollaxis(np.rollaxis(data[0:200].reshape(20, -1, size_img, size_img), 0, 2), 1, 3).reshape(-1, 20 * size_img)\n",
    "    plt.figure(figsize=(10,20))\n",
    "    norm = plt.Normalize(vmin=X.min(), vmax=X.max())\n",
    "    if epoch != \"\":\n",
    "        plt.suptitle(\"Epoch {}\".format(epoch))\n",
    "    else:\n",
    "        plt.suptitle(\"Original\")\n",
    "        \n",
    "    plt.imsave(\"images/{}.png\".format(filename),norm(X), cmap='gray');\n",
    "    plt.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Restricted Boltzmann Machine #\n",
    "- Contrastive Divergence (CD-1) training algorithm\n",
    "- Momentum\n",
    "- Minibatch\n",
    "- Weight decay"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "class RBM:\n",
    "    def __init__(self, n_of_features, n_of_neurons = 100):\n",
    "        xav = 0.1 * np.sqrt(1 / (n_of_neurons + n_of_features)) #xavier initialization\n",
    "        self.weights           = np.random.uniform(-xav, xav, size=(n_of_features, n_of_neurons))\n",
    "        self.bias_visible      = np.zeros((1, n_of_features))\n",
    "        self.bias_hidden       = np.zeros((1, n_of_neurons))\n",
    "        self.n_of_neurons      = n_of_neurons\n",
    "        self.n_of_features     = n_of_features\n",
    "        self.error             = 0\n",
    "\n",
    "    def wake_stage(self, training_set):\n",
    "        p_hidden_prob = self.sigmoid(-training_set @ self.weights - self.bias_hidden)\n",
    "        wake = training_set.T @ p_hidden_prob\n",
    "        hidden_states = 1*(p_hidden_prob > np.random.rand(p_hidden_prob.shape[0], p_hidden_prob.shape[1]))\n",
    "        return p_hidden_prob, wake, hidden_states\n",
    "    \n",
    "    def dream_stage(self, training_set, hidden_states):\n",
    "        visible_prob = self.sigmoid(-hidden_states @ self.weights.T - self.bias_visible)\n",
    "        visible_states = 1*(visible_prob > np.random.rand(training_set.shape[0], training_set.shape[1]))\n",
    "        n_hidden_prob = self.sigmoid(-visible_states @ self.weights - self.bias_hidden)\n",
    "        dream = visible_states.T @ n_hidden_prob\n",
    "        return visible_prob, visible_states, n_hidden_prob, dream\n",
    "    \n",
    "    def train(self, training_set, max_epoch = 20, lr = 0.1, batch_size = 100, momentum = 0.5, weightcost = 0.0001, verbose=False):\n",
    "        tr_original = training_set\n",
    "        tr_img = copy.deepcopy(tr_original)\n",
    "        print_img(-tr_original, \"original\")\n",
    "        dw  = 0 ; dbh = 0 ; dbv = 0\n",
    "\n",
    "        batch_ranges = range(batch_size, training_set.shape[0] , batch_size)\n",
    "        \n",
    "        for epoch in range(max_epoch):\n",
    "            batches = np.array_split(shuffle(tr_original, random_state = 123), batch_ranges)\n",
    "            if epoch > 5:    momentum = 0.7  \n",
    "            elif epoch > 10: momentum = 0.9\n",
    "                \n",
    "            for training_set in batches:\n",
    "                training_set = 1*(training_set > np.random.rand(training_set.shape[0], training_set.shape[1]))\n",
    "                \n",
    "                # CD_1 stages\n",
    "                p_hidden_prob, wake, hidden_states = self.wake_stage(training_set)\n",
    "                visible_prob, visible_states, n_hidden_prob, dream = self.dream_stage(training_set, hidden_states)\n",
    "                \n",
    "                # Weight update\n",
    "                dw = momentum * dw + (wake - dream)/ len(training_set) \n",
    "                dbh = momentum * dbh + (np.sum(p_hidden_prob) - np.sum(n_hidden_prob)) / len(training_set)\n",
    "                dbv = momentum * dbv + (np.sum(training_set) - np.sum(visible_states)) / len(training_set)\n",
    "                self.weights += lr * dw - weightcost*self.weights\n",
    "                self.bias_visible += lr * dbv\n",
    "                self.bias_hidden += lr * dbh\n",
    "\n",
    "            # Metric\n",
    "            error = self.error_full(tr_original)\n",
    "            delta = (self.error-error)/error\n",
    "            \n",
    "            self.print_reconstruction(tr_img, epoch+1, True)\n",
    "            self.print_reconstruction(tr_img, epoch+1, False)\n",
    "            \n",
    "            if verbose:\n",
    "                print(\"Epoch {}, Error {:.3f},  (delta error: {:.3f})\".format(epoch, error, delta))\n",
    "\n",
    "            if  epoch > 15 and error <= self.error and delta < 0.001:\n",
    "                break;\n",
    "\n",
    "            self.error = error\n",
    "            \n",
    "    def get_sample_of_hidden(self, training_set):\n",
    "        positive_hidden_probabilities, _, hidden_states = self.wake_stage(training_set)\n",
    "        return hidden_states, positive_hidden_probabilities\n",
    "            \n",
    "    def sigmoid(self, net):\n",
    "        return (1.0 / (1 + np.exp(net)))\n",
    "\n",
    "    def error_full(self, data):\n",
    "        _, _, hidden_states = self.wake_stage(data)\n",
    "        visible_prob, _, _, _ = self.dream_stage(data, hidden_states)\n",
    "        return np.mean(np.sum(np.square(data - visible_prob)))\n",
    "\n",
    "    def print_reconstruction(self, training_set, epoch, states=False):\n",
    "        if states == True: title = \"states_{}\".format(epoch)\n",
    "        else: title = \"probab_{}\".format(epoch)\n",
    "                \n",
    "        _, _, hidden_states = self.wake_stage(training_set)\n",
    "        visible_probabilities, visible_states, _, _ = self.dream_stage(training_set, hidden_states)\n",
    "        if states: print_img(-visible_states, title, epoch)\n",
    "        else: print_img(-visible_probabilities, title, epoch)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multi-layer Perceptron #\n",
    "To classify the MNIST's digits we can train a simple classifier using the sklearn library. \n",
    "\n",
    "After the training step and the classification on the test set, we plot the confusion matrices and the learning curves.\n",
    "\n",
    "(Change verbose to True in order to have some output during the training)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def classify(tr_images, tr_labels, ts_images, ts_labels, title):\n",
    "    classifier = MLPClassifier(verbose=False, early_stopping=True, max_iter=250, n_iter_no_change=200)\n",
    "    history = classifier.fit(tr_images, tr_labels)\n",
    "    predicted = classifier.predict(ts_images)\n",
    "    print(\"Report %s:\\n%s\\n\" % (classifier, metrics.classification_report(ts_labels, predicted)))\n",
    "    \n",
    "    disp = metrics.plot_confusion_matrix(classifier, ts_images, \n",
    "                                         ts_labels, cmap=plt.cm.Blues, \n",
    "                                         normalize='true',values_format='.2f')\n",
    "\n",
    "    disp.figure_.suptitle(\"Confusion Matrix (TS) {}\".format(title))\n",
    "    plt.savefig('images/confusion_matrix_TS_{}.eps'.format(title), size=(10,10))\n",
    "    \n",
    "    disp = metrics.plot_confusion_matrix(classifier, tr_images, \n",
    "                                         tr_labels, cmap=plt.cm.Blues, \n",
    "                                         normalize='true',values_format='.2f')\n",
    "\n",
    "    disp.figure_.suptitle(\"Confusion Matrix (TR) {}\".format(title))\n",
    "    plt.savefig('images/confusion_matrix_TR_{}.eps'.format(title), size=(10,10))\n",
    "    \n",
    "\n",
    "    fig, axes = plt.subplots(nrows=1, ncols=2)\n",
    "    fig.suptitle('Learning curves')\n",
    "\n",
    "    axes[0].title.set_text('Loss') \n",
    "    axes[0].plot(classifier.loss_curve_)\n",
    "    axes[1].title.set_text('Accuracy') \n",
    "    axes[1].plot(classifier.validation_scores_, c=\"orange\")\n",
    "    axes[0].set_ylim([0, 1.0])\n",
    "    axes[1].set_ylim([0.7, 1.0])\n",
    "\n",
    "    fig.tight_layout()\n",
    "    fig.subplots_adjust(top=0.87)\n",
    "    plt.savefig(\"images/final_plot_with.eps\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Training of the RBM #"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "rbm = RBM(tr_images.shape[1], 100)\n",
    "rbm.train(tr_images, lr = 0.1, batch_size = 100, max_epoch=20, momentum=0.5, verbose=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Feature extraction and classification #\n",
    "Transform the training set and the test set using the RBM (just take the hidden probabilities associated to them). Use the train set to train the MLP classifier, and the test set to benchmark it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/gabriele/.local/lib/python3.7/site-packages/sklearn/neural_network/_multilayer_perceptron.py:571: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (250) reached and the optimization hasn't converged yet.\n",
      "  % self.max_iter, ConvergenceWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Report MLPClassifier(activation='relu', alpha=0.0001, batch_size='auto', beta_1=0.9,\n",
      "              beta_2=0.999, early_stopping=True, epsilon=1e-08,\n",
      "              hidden_layer_sizes=(100,), learning_rate='constant',\n",
      "              learning_rate_init=0.001, max_fun=15000, max_iter=250,\n",
      "              momentum=0.9, n_iter_no_change=200, nesterovs_momentum=True,\n",
      "              power_t=0.5, random_state=None, shuffle=True, solver='adam',\n",
      "              tol=0.0001, validation_fraction=0.1, verbose=False,\n",
      "              warm_start=False):\n",
      "              precision    recall  f1-score   support\n",
      "\n",
      "           0       0.98      0.98      0.98       980\n",
      "           1       0.99      0.99      0.99      1135\n",
      "           2       0.95      0.97      0.96      1032\n",
      "           3       0.95      0.96      0.96      1010\n",
      "           4       0.95      0.98      0.96       982\n",
      "           5       0.97      0.95      0.96       892\n",
      "           6       0.97      0.97      0.97       958\n",
      "           7       0.96      0.97      0.96      1028\n",
      "           8       0.96      0.94      0.95       974\n",
      "           9       0.97      0.92      0.95      1009\n",
      "\n",
      "    accuracy                           0.96     10000\n",
      "   macro avg       0.96      0.96      0.96     10000\n",
      "weighted avg       0.96      0.96      0.96     10000\n",
      "\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "_, hidden_probab_wake_tr = rbm.get_sample_of_hidden(tr_images)\n",
    "_,hidden_probab_wake_ts = rbm.get_sample_of_hidden(ts_images)\n",
    "\n",
    "classify(hidden_probab_wake_tr, tr_labels, hidden_probab_wake_ts, ts_labels, \"Using RBM\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Classification using the standard dataset (without the RBM)#"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/gabriele/.local/lib/python3.7/site-packages/sklearn/neural_network/_multilayer_perceptron.py:571: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (250) reached and the optimization hasn't converged yet.\n",
      "  % self.max_iter, ConvergenceWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Report MLPClassifier(activation='relu', alpha=0.0001, batch_size='auto', beta_1=0.9,\n",
      "              beta_2=0.999, early_stopping=True, epsilon=1e-08,\n",
      "              hidden_layer_sizes=(100,), learning_rate='constant',\n",
      "              learning_rate_init=0.001, max_fun=15000, max_iter=250,\n",
      "              momentum=0.9, n_iter_no_change=200, nesterovs_momentum=True,\n",
      "              power_t=0.5, random_state=None, shuffle=True, solver='adam',\n",
      "              tol=0.0001, validation_fraction=0.1, verbose=False,\n",
      "              warm_start=False):\n",
      "              precision    recall  f1-score   support\n",
      "\n",
      "           0       0.98      0.99      0.98       980\n",
      "           1       0.99      0.99      0.99      1135\n",
      "           2       0.97      0.97      0.97      1032\n",
      "           3       0.97      0.98      0.97      1010\n",
      "           4       0.98      0.98      0.98       982\n",
      "           5       0.98      0.97      0.98       892\n",
      "           6       0.98      0.98      0.98       958\n",
      "           7       0.98      0.97      0.98      1028\n",
      "           8       0.96      0.97      0.97       974\n",
      "           9       0.98      0.97      0.97      1009\n",
      "\n",
      "    accuracy                           0.98     10000\n",
      "   macro avg       0.98      0.98      0.98     10000\n",
      "weighted avg       0.98      0.98      0.98     10000\n",
      "\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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B0w1SXv3SrTYCJMfvNClxh174Iy5yFvAIkAw8o6r3REqfVK+l+rFKx/ZPbZUOwwBnlY6srM+q1dmV1Kid1ulzo6e0v7z/pyxVrf7SIFHg6+BbVZ0DzPHzGoZhHGpsmpRhGImGTZMyDCOhsJqaYRgJQw2OQfOCBTXDMKLHFok0DCNxsBcFnknv3tEXk5SmfUbHXBNg+7LHfdE1jLjHmp+GYSQMcb6emgU1wzCixJqfhmEkGvaiwDCMhML61AzDSBjEmp+GYSQaVlPzjl/uOUMGdOe+2y50Xao+5pHnKnCpmnBlqUvVhOdCXKpGcsZJxS5Vb/P6u/66VAXNmShIukHKq5+61UXiOKj56ST1DJAHrPJ6Tnp6pi+uPPUyRrsuVRO0Ye+bdNnqTdrrvL9oatqNJduMuVk66k/Pa2rajTr0t/9wXKrSbtQRN/7TcanK/IM263+r41I18DZNTbvRHI8CphukvMazm1RSkyO13gXPeNpIJDcp4FkcizzPFNDAF/eczOOOYt2mbWzc4rpUvbucs04OX0G0W+c2LPrsS6AKl6qvt/jqUhU0Z6Ig6QYpr37qVhsRJMnbVhP4FtRUdSHwUzTnHKC2L+45XtZ6X/3VFoafmgbA8FOLXarquy5V3UtdqnofU3IdczwKlm6Q8uqnbiwQEU9bTVDjfWoici1wLUDLLv1qLB93/eN1Hhh3EZcP78fHK9a6LlVFfLA0h4weRzLvmdvYtn23uVQZBvHdp1bj72VD3aSaNUr1xT3Hyy/e99t28ptxT3Pylfcz5Z9lXarmMfiKv3L+6McRhG82+udSFTRnoiDpBimvfurGgniuqdV4UAulLrt9cc9Znr2RLh1DXKqGZjB3YXjfRLhL1a/KuFTVB1yXqq7+ulQFzZkoSLpByqufutVGothqgBpvfoYi4o/bT2FhEeMeeJmZj95IcrIwfZbrUvX7sx2XqoVfOC5VN45Atdil6mXAdal6KtSl6jnfXaqC5EwUNN0g5TVe3aSEmquFecE3NykRmQGcAjQHfgAmqurUSOdkZvbWxUs/i3lebOkhw3CIhZtUyhGdtdFZUzyl3f7CFYnjJqWql/mlbRhGzRLPNbW46lMzDCMAxLBPTUTOFJEvRWStiNxRwfGOIvKBiKwQkf+6XsIRsaBmGEbUxOLtp4gkA08Aw4AewGUiUnYu15+Bl1U1HbgU+GdVebOgZhhGVBS/KIjBkI6+wFpVXaeq+4CXgJFl0ijQyP27MZBblWhcvf00DCMYRDEFqrmIhL79e0pVn3L/bgdsCjm2GSg7An8S8I6I/AGoD5xe1QUtqBmGER0S1YuCbdV8+3kZ8KyqPiQiA4BpInK8qlY6rSeugpoCfgwx8WvoRdMTb4u55k+L/xZzTYjvt1UV4ddQIz/wK6tJNTQh3Asxep62AB1CPrd394VyDe7CGKq6RERScYaJ5VUman1qhmFETYz61JYBXUWkk4jUxnkRMKtMmm+BIe41uwOpwNZIonFVUzMMI/6J1YwCVT0gIqOBeUAy8IyqrhaRu3HWYZsF3Ab8r4jcitOYG6VVVOMtqBmGET0xahmr6hxgTpl9E0L+zgYGRqNpQc0wjOgQSEqK354rC2qGYURNPL94irug9t6SbO58aKZrNDGAW66qwGhi0jQ+z9lE08b1eeaeq0uMJv7+7DslRhP33XZhybLb4I+BxZB+3bjvlnNJTk5i2uylPDLt/TDNDq2b8tidl9C8SX3HzGXyi+Ru3clJGV2496bSMYZdj2zJNRNfYM7CVYErA191fSgHv8p2/pJsxj88k6KiIq4cUbHuDZNLdadOcXR/2pnP1XdMZcWajVx6dj8euP3isPPi1XilppYV8oSPxisdgA+AbGA1cHNV56S5xivZ6/N0R/4+zbzwHl2es0X37Csq2R578UO9bvKLumdfkU57c5leOvZp3bOvSJfnbNHMC+/R7bv36pr1eXrs2RP154IDumdfkW/GGNkbtmq3kVO04YDbdVn2Fu110f2a2mdMyTZj3kodNeFFTe0zRode9099dvaysOOpfcZo69P+pLk/5mvTk/6oqX3G6M8FBwJVBn7p+lEOfpXtrj2O7up1ebp9t6ObtWaL5u8tKtkene7o5u8t0mmzHd38vUWat6NA5y/9Wh+fsVBvnPJS2DnxarxSq0UX7TD6DU8bCWa8cgC4TVV7AP2BGyuY1xVGAQ3o1L45R7VzjSbOyGTuwi/C0sxZ8AWXlhhNpLFw2VeoKnMXfsH5Z2SWGE10at+crNUbAf8MLNZt/pGNuT85Zi7vreCsQceFaXY7qhWLstYCsChrLcMGHV/uO488rRfvLcmhYO9+N68bA1UG/unGvhz8Ktvl2eG65w0trzt3YanuiBDd+nXr0D+tC3Vql280xavxitfhHAm38q2qfqeqy92/fwbW4EyLqJRyxistm/Dd1h1haZyluZsAZY0mdlR6rl8GFlt+KM1b7tad5c1c1uYy/BTHlWr4yT1pVD+Vpo3qhaU5//Q0Zob4iEb6HvFYBv7pxr4cfCvbPG+6bVuW142EGa8cHIfkFYaIHAWkA0sPxfXihbsen83AtM4seHYMA9M7syVvR5hpS6sjGtKjcxvmL/2yBnNpGNFzWFrkFSMiDYCZwC2ququC49eKyGci8ln+zrwyZhE7aNOiSVh6x1DC+RUMN5poUum5fhlYFP+iA7Rt0bgCM5dd/ObO5zh51MNMeXIuALt2/1Jy/Nwhaby58AsOFJYGukjfIx7LwD/d2JeDb2Xb0ptubl553UiY8crB4WtQE5FaOAFtuqq+VlGaUDep1o1TWLcpxGjinSzOHNQzLP2wwT15qcRoYiWDejtGE2cO6slr72SVGE2s27SVzOOOBPwzsOjSvjkd2zRzzFxOT2fuR6vDNMPMXH4zhOlvfhp2/ILT05n57oqwfRk9OgaqDPzTjX05+FW26d1d3VxH9/V3s0rMsEPLoFh3VohuJOLZeCWeg5pvQzrE+UZTgTWq+rC3c+CB2y/iwpv+SWGRcsU5rtHEk2+R3r0jwwb35MoRA7hu4vNknj+Zpo3q8XSY0UQGAy65l5TkJB4Yd5HvBhbjHn6NmX+/1jFzefNTctb/wPjf/oqVOZuZ+9FqTsrowoTrznLMXFau4/aHZpZ81w6tm9KuVRMWr1gXVgYpKcmBKgNfdX0oB7/K9v6xF3GRq3v5Of05tnMb7nvyLdJCdK+f9Dy9L5hMk0b1eHrK1SX3PO3cifyc/wv79x9gzoIvePXRGzi2c5s4Nl5x/q3GK34ar5wELAK+AIrbV3e60yIqJCOzty7+ZJkfeYm5JtgqHX5iq3T4s0pHLIxXUlsfox1+/aintGv/NiyhjFc+Ir6H6BmGcZDE87JIcTejwDCMOEfiu/lpQc0wjKgQrKZmGEaCYTU1wzASinh+8WRBzTCM6LA+Ne8441/iuLTK4Mfwi2YDbo25JsD2Tx7xRdcvgvQcOKtMHz4IYotEGoaRWMTzb44FNcMwoiaea9IW1AzDiA7rUzMMI5GI975vC2qGYURNHMc0C2qGYUSPzSiIgiA5Hh2sM9FPO/IZNX4qK7I3ctnw8g5CQ/ofy323nk9ykjBt1ic8Mm1+2PEOrZvy2J8uo3nTBo5L1cRp5LoLVE4efQ5DT+xBUlISH376JXc8XLqMXZDK1rd7FiDnKz/zWy0kvpuffrpJpQKfAp/juElNruqcdNdNKgiOR8WaB+NMtHVngb7/6df6xIyFOvqel8LOqdfnFs1ev1W7nXO3Nuw3Rpdlb9ZeF9yrqZk3l2wz3l6ho+56QVMzb9ah1z6uz876VFMzb9bBo/6uH2Z9o/X63KL1+tyiC5av1yG/e0xTM28OnJuUn/csCM5XfjmAxcJNqn67Y7TffR962kgwN6m9wGmq2gtIA84Ukf6RTiigQWAcj7JWbzhoZ6ISB6E65SvKmT2OZN3mbWzM/dFxqXp3BWeVWUW1W6dWLPrsawAWZX1dssqqKtSpXYvatVKoUyuFWilJbP3pZ9/KIGi6QXK+8rNsq8/h6yalqrrb/VjL3SIOvS7nJhXHjkfl93t3JopEmxaN2ZJXdr37Mi5VX+cy/BRnWefhp5xQ4lK1bNUGFmV9Tc6bd5Pz1t28vzSHrzb84FsZBE03SM5XfpZtLBDxttUEfnsUJIvISiAPeFdVy7lJhRqv7NpVzpfFqIC7HnuDgRldWPDcWAamd3FdqpRO7ZvT7ahWHDdiIj3OmcigzGMY0KtzTWfXSDTEeVHgZasJfA1qqlqoqmlAe6CviJRz8w01XmnWKDUwjkfl93t3JorEd1t30q5l2V/uClyq7vg3J1/1N6b8z1sA7NpdwPCTe7Js1UbyC/aRX7CP95asoU/Po3wrg6DpBsn5ys+yrS7F49QOu+ZnKKq6A/gAODNSurrsDozjUUaPIw/amSgSy9d8S5cOIS5VQ9OZu2hVWJowl6qrTmf6bOcam3/YwcCMLiQnJ5GSnMTA9C4lzc/guUn5c8+C4nzlZ9nGgngOan66SbUA9qvqDhGpCwwF7o98DoFyPDpYZyKAXiNLHYTeWvAFM10HocLCIsb9bSYz/3EdyUlJTH9zKTnrv2f874axMudb5i5azUkZRzPhhuGoKh+v/IbbH3wVcP6xDM7syuLpf0RVmf9JDm+7tn2BdJPy454FyPkqXt2kIL4H3/rpJnUC8ByQjFMjfFlV7450TmZmb1289DNf8uMHfpSdLT0UPHz8NxRzzVi4STXscKxm3vaMp7QLbh2YUG5S/wXS/dI3DKOGsAnthmEkEs4ikfEb1eJ3+UrDMOKWJBFPW1WIyJki8qWIrBWROypJc7GIZIvIahF5sSpNq6kZhhE1sWh+ikgy8ATOS8TNwDIRmaWq2SFpugLjgYGqul1EWlalazU1wzCiQiRmQzr6AmtVdZ2q7gNeAkaWSfM74AlV3Q6gqnlViVpQMwwjapLE2wY0L54x5G7Xhsi0AzaFfN7s7gvlGOAYEVksIp+ISMSxrhCh+SkijxFhrqaq3lSVeKLjxyt3v4ZeNO13sy+625f+wxfdIOHXINOiotgPFYmVYhQvCrZVc0hHCtAVOAVnZtJCEenpDuiv9ITKCM6AMcMwDhmC8wY0BmwBOoR8bu/uC2UzsFRV9wPrReQrnCC3rDLRSoOaqj4X+llE6qnqnmhzbRhG4hGjER3LgK4i0gknmF0KXF4mzX+Ay4B/i0hznObouoh5q+qqIjJARLKBHPdzLxH5Z/T5NwwjIfD4kqCqZrmqHgBGA/OANTizjlaLyN0iMsJNNg/40Y1BHwC3q+qPkXS9DOl4BPgVMMvNyOciMtjDeYZhJCix6kZU1TnAnDL7JoT8rcAYd/OEp3FqqrqpTNQt9HoBwzASCwFPA2trCi9BbZOInAioiNQCbsapKhqGcZgSz9OkvAS164B/4IwfycVp497oV4aC5Ezkl65feR3S/1juG3M+yUlJjkvV8++F6XZo3ZTH/nw5zZs0YPuufH4/aRq5ecUuVSMYOrAHSSKBdqkKUl4B5i/JZvzDMykqKuLKERW7VN0wudSlauoU17FsZz5X3zGVFWs2cunZ5R3LqkNNLtXtCb+dXXCWHloBvFlV2iC5SQXN8ahe75sdl6rhk7Vh31tdl6p7NDXjppJtxtvLddSfp2lqxk069HePOS5VGTfp4Kse1g8/+0br9b5Z6/W+WRcsX6dDfvuopmbcZGXr4/O1a4/jUrV6XZ5u3+24VGWt2aL5e4tKtkenOy5V+XuLdNpsx6Uqf2+R5u0o0PlLv9bHZyzUG6e8VJI+PQZuUk2P6q4XP7vc00Y8ukmJSGcRmS0iW0UkT0TeEJFoFr733FwNkpuUX7p+5dVxqdoa4lK1vAKXqtaVu1TVCXWpSg6kS1WQ8gqwPDvcpeq8oeVdquYuLHWpGlGRY1ltf6Z3i8etJvAyTepF4GWgDdAWeAWY4UVcRNoDZwNPe0kfJDcpv3T9ymublqVr5DsalbhUndoLqMSl6q27yZnzF97/JJguVUHKK8B3ed5cqtq2jM6xLBbE83LeXoJaPVWdpqoH3O0FHKNiLzwCjAOKKktgblLxw12P/oeB6V1Y8PztDMw4urxL1TkT6TF8AoN6d2VAmrlUHbETiBUAACAASURBVK44bz89z/085FQa1ESkmYg0A+aKyB0icpSIHCki4ygzrqSS84cDeaqaFSldUN2k/NL1K6/f5ZX6TjoalblUPcPJv3mQKf96E3Bdqk45gWWrNoS7VB1/lJWt389XS28uVbl50TmWVRvxZo8XjxZ5WTjzPy8Gfo8zmvdD4HrgEg/aA4ERIrIBZ0mR00TkhUgnBMlNyi9dv/LquFS1CHGpymDuwkguVUOZPvsTADZ/v52B6UeHuFQdHUiXqiDlFSC9u+tSlevovv5uVkk/Z6husUvVLI+OZbEgnpufkeZ+dqqOsKqOx1ncDRE5BRirqldGOidoblJBcjwqcal69HrHpWr2J45L1bXDWLlmE3MXreKkzKOZcMM5jkvVim+4/cFXANelqrfrUgXMX7ImsC5VQcprSkoy94+9iItcl6rLz+nPsZ3bcN+Tb5EW4lJ1/aTn6X3BZJo0qsfTU0ody9LOLXUsm7PgC1599AZP/3arorj5Ga94cpMSx4S4ByF9aar6vOeLlAa14ZHSBc1NKkjY0kPBw4+lh04a0Ifl1XSTat75OD3n3pc8pX32shPiz01KRCbirGXUA6cvbRjwEeA5qKnqhzhNV8MwEoA4rqh5evt5ITAE+F5VrwZ6AbHxrzcMI3CIQHKSeNpqAi8j8wpUtUhEDohIIyCP8IXdDMM4zKiplwBe8BLUPhORJsD/4rwR3Q0s8TVXhmHENXEc06oOaqpa/Mrkf0TkbaCR675uGMZhiODN07OmiGS8khHpmKou9ydLhmHENXG+SkekmtpDEY4pcFqM82IAhT68xgf/hl40HXi7L7rbFz/oi64feBkWdTD4MSI/VoqB7FNT1VMPZUYMwwgGAiQHMagZhmFURjzPKLCgZhhG1FhQMwwjYXCW847fqOZl5VsRkStFZIL7uaOI9PU/a4ZhxCuBXE8thH8CA3BckgF+Bp7wLUeGYcQ9xeYrVW01gZfmZz9VzRCRFQCqul1EavuVoaC5/fihO39JNneGOAjdXImD0H9dB6GnyzgIrXQdhO4v4yDkm0tVv27cd8sIx6Vq9qc88sIHYbodWjXhsTsvdl2q9vD7u2eQu3UnJ2V04d6bRpSk69qxBddMnM6cRat9y69vz8GSbO58aKarW7Hr0/WTSl2fnrnHvWc78hk1fiorsjdy2fDyrk9+5bc6CJASx81PL25QS3EcoZa7n1sAKzw6SW0AvgBW4sFVxtykCnWn6yC0al2e/hTiILR7b1HJ9uj0D/X3k1/U3XuL9PnZy/SSsU/r7r1F+sOOAn1v6df6mOsgFHqOby5V/W/X7A3btNu592rDE/+oy7K3aK+LH9DUvmNLthnzVuqoiTM0te9YHXrdv/TZ2Z+FHU/tO1ZbD7lLc3/M16aDxmtq37GBcpP6ucC5Z9nr83RHvnPPluds0T37ikq2x150XJ/27CvSaW86rk979hXp1p0F+v6nX+sTMxbq6HteCjvHj/xmxMBNqvXRx+mdc770tHn5d3/I3aSAR4HXgZYicg/OskP3RhE3T1XVNC9rKpmb1IaDchBaVMZBKLUCByHfXKq6d2Td5m1szP3Jcamav5KzBh0XptutUysWZa0FYNHybxhW5jjAyFNP4L1PcijYu9+3/Pr3HITfs/PPKH/P5iwovWcjK3J9qnPo7ll1EXGmSXnZaoIqg5qqTscxT7kP+A44V1Vf8SMz5ia1k+/ydtDWg4NQuygdhHxzqWrRiC15O8I0yrtUfcfwk51lqIeffHyJS1Uo55+exsx3V/qaX/+eA2+uT8UeETV9z2JBPPepeXn72RHYA8wGZgH57j4vKPCOiGSJyLWV6JubVIJz1xNvMjC9Mwv+fQsD0zq7LlWlBmOtjmhIj86tmb/0yxrMpREN8fz208uLgrdwgpPgLOfdCfgSKN+GKM9JqrpFRFoC74pIjqouDE2gqk8BTwF0zzhFvbrytGvV1Be3n5rWLVJHp3R/xQ5CW9wanVcHIb/K4Lutu0pqjcUaFbpU3ekslFy/bm3OOaUnu3b/UnL83NN68ebCVRwoLA10fuXXn+fAm+vTlh92lNONhF9lUF0EamwBSC94aX72VNUT3P93BfricT01Vd3i/j8Pp18u4vg2c5M6qkIHoTNj4CDkm0tVzia6tG9OxzZNHZeqIWnM/Sg7TLdZ43qlLlW/Po3pby0LO37B0DRmvrcybF+w3KTce1as+04WZw4Kv2fDBpfeszdq+J5VG4+1tHiuqYWhqstFpF9V6USkPpCkqj+7f58B3B35nOC5/cRcV4S/ug5CRZU4CF0xYgA3THqePq6D0P+GOAilV+Ag1K1zG9/KoLCwiHF//w8zH/4dyclJTH/zU3LW/8D4357BypzNzP0om5PSuzDhumGowsefr+P2h14vyW+H1k1p17IJi1esC3sWAucmdftFXOi6Pl1xjqv75Fukh7g+XTfxeTLPn0zTRvV4+p7Se9ZrZOk9e2vBF8x89AaO9fGexQKJY5eCKt2kRGRMyMckIAM4QlV/VcV5nXFqZ+AEzxdV9Z5I55iblH9LD/nVXLClh/xbesiPqUgD+/Umq5puUu279dTR//qPp7Tjhxwdf25SQMOQvw/g9LHNrOokVV2HY9JiGEaCEcddapGDmogkAw1Vdewhyo9hGAEgkBPaRSRFVQuBgYcwP4ZhxDmORZ63rWotOVNEvhSRtSJyR4R0F4iIikiVTdlINbVPcfrPVorILOAVoGS0oKq+VnWWDcNIRGIxW8BtCT4BDAU2A8tEZJaqZpdJ1xC4GWfKZpV46VNLBX7E8SQoHq+mgAU1wzgMEWLWp9YXWOv2vyMiLwEjgewy6f4C3A94eisVKai1dN98rqI0mBXjz+sewzACQRQVteYiEjqk4Sl3wD1AO2BTyLHNQNhwMdfVroOqviUi1Q5qyUADKjag8SWoKf68Ho/nTs2y+DX0wq9hBz999IAvuk0HjKk60UGwfcnDMdcM0vMVG4Qk7+PUth3skA4RSQIeBkZFc16koPadqkYcLGsYxuGHELPJ6luADiGf27v7imkIHA986P5wtAZmicgIVa10QGukoHa4/fwYhuEFgZTYtCiWAV1FpBNOMLsUuLz4oKruBJqXXFbkQ2BspIAGked+DqlObg3DSEyKa2rVXXpIVQ8Ao4F5wBrgZVVdLSJ3i8iIyGdXTiQz458OVtQwjMQmVgtAquocYE6ZfRMqSXuKF02zyDMMI2ri+d1I7Kbtx4j3lmTT98K/kHn+ZB557p1yx/fu28//u/MZMs+fzOlX/41vc38E4Kcd+Yy4/lE6nHwb4x58ubzux9n0ueBuMs6bxN+frUR3/DNknDeJ00c9WKILjoFFxnmT6HPB3cxfEj6Exg9d3/LqV9n6oDuk/7F8+tIdZL1yJ7f8+rRymh1aN+U/j13HR9PGMvuJG2gbslbY5BuH8/H0cXwy44/89dbzwvMaoOfAT93qIDiBw8tWI/hpgAA0AV4FcnDazAMipU9zjVeCYGDhl/FK0MxB/NLNXr9Vu434izbsP9Yxc7nwr5ra+9aSbca8FTpqwnRN7X2rDv39E/rsrGWa2vtWHXz1P/TDrHVar+8Yrdd3jC5Yvl6H/O5x57zMWwLzHPilGwvjlaO699Tnln3raSNOjVeqwz+At1X1WJwVO9ZESlxAg0AZWJg5iH+6YWYu763grMHHhx3vdlRrFn3mmrlkrWWYe1xVqVM7hdq1UqhTK4VaKcls/eln9ywNzHPgp251cWYUBNh45WARkcbAYGAqgKruU9Udkc4pZ7wS5wYWZg7in264mcuO8mYua3MZfkqxmUvPEjOXZas2smj5WnJmTyLnzUm8vzSHrzbmOScpgXkO/NSNBeJxqwn8rKl1ArYC/xaRFSLytLsCrmFUm7sem8XA9C4seG4MA9O7lJi5dGrfnG5HtuK4kZPpMWIygzK7MqBXp5rObsIRaDepapCCs8rHv1Q1HWeFj3JLi4S6SeXvzPNsYAH4YmBRVjdWxitedf3Lq3dzkLK6kfBLN9zMpUnFZi7jn+Xkqx5mypPOiIBdu39h+Mk9WbZ6I/kF+8gv2Md7n+TQ5/ijnJPEu/FK2bwe6ufAT93qI4h422oCP4PaZmCzqhYvF/IqTpALQ1WfUtXeqtq7deOUQBlYmDmIf7pdOrSgY5tmjpnL6enMXbQq7HizxvVLzVx+M4Tpb34KwObvtzMwvQvJyUmkJCcxML0zX238wT1LAvMc+KlbXeL97adv49RU9XsR2SQi3VT1S5wZChHfK4sQKAMLMwdp45vuuIdeY+Yj15KcFGLm8rszWblmE3M/Ws1JGV2YcP3ZqCofr1zH7X9zVph/44PPGdy7K4tfuB1VZf4nObxd7G4lEqjnIJ6NV2rqJYAXqjReqZa4SBrwNFAbWAdcrarbK0ufkdlbF3+yrLLD1clHzDWDhp/32Q+anXibL7p+rNIRJGJhvNLluF56/4tve0p7UVrbuDReOWhUdSVwSL+QYRj+Utz8jFdsmpRhGFETz60fC2qGYURN/IY0C2qGYUSJAMlWUzMMI5GI45hmQc0wjGgRJI4boBbUDMOIGqupecRZJjj2peXXGC0/ZP16WOL5bVVF+DWezA+XKr/y6sdzGwtFZ0hH/D5PcRXUDMMIADU4Wd0LFtQMw4iaeJ4mZUHNMIyocBaJrOlcVI4FNcMwosbefhqGkVDEcesz/oLaex9nM/6hVyksKuLXI0/k1lFnhB3fu28/10+cxsqcb2nWuD7P3Pv/6Nj2CMBxz3lh1hKSk5L469gLGTKgR6nukmzufGimqzuAW66qQHfSND7P2UTTxvV55p6rS3T//uw7Jbr33XYhQwZ0B2D+kmzGPzyToqIirhxRseYNk0s1p05xNH/amc/Vd0xlxZqNXHp2Px64/eLwMvAhr76WbYB0h/Q/lvtuOZfk5CSmzfqER6a9H6bZoXVTHvvTJTRv0oDtu/bw+0nTyd26k5Myjubem0eWpOt6ZEuumTCNOQtX+VsGPj0L1SWea2p+Okl1A1aGbLuAWyKdk+66ScWTk9LynC2aeeE9un33Xl2zPk+PPXui/lxwoERz9bo83b7b0cxas0Xz9xaVbI9OdzTz9xbptNmOZv7eIs3bUaDzl36tj89YqDdOeSnsHD/yGjRHLT91D9alKnRrfdqfNPfHfG06cJym9r41Lh3AKnsW0mPgJtXtuF664MsfPW0kkpuUqn6pqmmqmgZkAnuA1yOdU0CDuHNSmrvwC84/I7NEt1P75mSt3lhO87yh5TXnLizVHFGRi1Lt2LozVZZXRzdYjkd+6R6sS1UoI089gfeWrKFg736fy8CfZ6HaeHSSSjg3qTIMAb5R1YilWs5NKg6clCo716tm25aHzp0p0rlBczzyS/dgXapCOf/0dGa+u6Lkczw6gHk5tzocrm5SoVwKzKjoQKjxyq5duw5RdgyjYipzqSqm1REN6dGlDfM/yanBXNYsh63vZzEiUhsYAbxS0fFQ45VmjVLjzkmpsnO9aubmHTp3pkjnBs3xyC/dg3WpKubcIWm8ueALDhSWBrp4dADzcm51ONxrasOA5ar6Q1UJ67I77pyUzhzUk9feySrRXbdpK5nHHVmqmetovv5uFsMG9yyX12LNWYfAnamyvDq6wXI88kv3YF2qirlgaEZY09PfMvDnWYgJcRzVDsWQjsuopOlZFpH4c1JydDMYcMm9pCQn8cC4i0p07x97ERe5mpef059jO7fhviffIi1E8/pJz9P7gsk0aVSPp6eUuiilnVvqojRnwRe8GgN3pkh5DZrjkV+6B+tSBc5wj3atmrB4xTdhz62vZeDDsxAL4nmalN9uUvWBb4HOqlql531mZm9dvPSzmOfDVukI3iodfnG4r9IxsH8fllfTTap7z3R9/o0PPaXt26VJwrlJ5QNH+HkNwzBqgDj+jYy7GQWGYcQ3TndZ/EY1C2qGYURHnK+nFs+epIZhxCmxevkpImeKyJcislZE7qjg+BgRyRaR/4rIfBGp8hWuBTXDMKJEEPG2RVQRSQaewBn21QO4TER6lEm2AuitqicArwIPVJU7C2qGYUSNiLetCvoCa1V1naruA14CRoYmUNUPVHWP+/EToH1VonHVp6b48xrbr+EMfsj6OcTGD/zKr1/3zI/hF34MEwF/8hqLUo1yXG1zEQkdp/WUqj7l/t0O2BRybDPQL4LWNcDcqi4YV0HNMIyA4D2qbYvFODURuRLoDZxcVVoLaoZhRE2MhnRsATqEfG7v7gu/lsjpwJ+Ak1V1b1Wi1qdmGEbUxKhPbRnQVUQ6uQtfXArMCr+OpANPAiNUNc9L3qymZhhGdMRonJqqHhCR0cA8IBl4RlVXi8jdOCvmzgIeBBoAr7j9rN+q6ohIuhbUDMOImljNKFDVOcCcMvsmhPx9erSaFtQMw4gKIb5nFMRdUDMnpQCWQYDy61cZBM2lqrrEcUzzz03KHb90K7AaWIWzplpqpPRprpvU4eykFDQ3qSDl168yqNd3TGBcqjJi4CZ13Anpmp2729NGIrlJiUg74CacKQ7H43QEXhrpnAIaHPZOSsFzkwpOfv0qg8weHQPlUhULDmePghSgroikAPWA3EiJy7lJHYZOSsFzkwpOfv0qgzYtGgfKpSoWxPFq3r76fm4B/oaz8u13wE5VfadsulA3qZ/NTcpIUBLOpSqOo5qfzc+mOJNTOwFtgfruVIcwQt2kmpZ1kzoMnZSC5yYVnPz6VQbfbd0ZKJeq6lK8SKSX/2oCP5ufpwPrVXWrqu4HXgNOjHRCXXYf9k5KwXOTCk5+/SqD5Ws2Bcqlqtp4nE1QU8M+/BzS8S3QX0TqAQU4Lu0RXVVEOOydlJKSJHhlEKD8+qFZWFgUKJeqWBDPQzr8dpOaDFwCHMBZ7O23kSakZmT21sWfLPMjHzHX9IugLeUTtPz6QZCWHhrYrzdZ1XST6pmWqW+8u9hT2i4t6yacm9REYKKf1zAM49ATz785cTejwDCM+KYmh2t4wYKaYRjRE8dRzYKaYRhRY76fhmEkFNanZhhG4iCQZEHNG846TXFcWocAv75/UZE/Qy+S4vnprgA/hqD89PFDMdcEaHribTHX3JuzOUZK8Xvf4yqoGYYR/9gikYZhJBxxHNMsqBmGET1WUzMMI6GI575vC2qGYURN/IY0C2qGYURJTS4r5IW4C2pBcn3yS9evvM5fks34h2dSVFTElSMqdn26YXKp69PUKY7r008787n6jqmsWLORS8/uxwO3XxzYe3awzlc/7chn1PiprMjeyGXDKygDnxy1hvTrVupSNXtpxS5Vd15C8yb1HZeqyS+6LlVduPemMi5VE1/g9dXEhHieUeC3m9TNOE5Sq4Fbqkqf7rpJBcH1yS9dv/K6a4/j+rR6XZ5u3+24PmWt2aL5e4tKtkenO65P+XuLdNpsx/Upf2+R5u0o0PlLv9bHZyzUG6e8FHZOEMv2YJyvtu4s0Pc//VqfmLFQR9/zUtg5fjlq1et3m2Zv2KrdRk7RhgNud1yqLrpfU/uMKdlmzFupoya8qKl9xujQ6/6pz85eFnY8tc+YUpeqk/6oUq9Vtd2keqVnaN7P+z1tJJib1PHA74C+QC9guIgcHemcAhoExvXJL12/8ro8O9z16byh5V2f5i4sdX0aEeL6VL9uHfqndaFO7fIV+6CV7cE6X5WUQZ2KysAfRy3HperHcJeqQceF6XY7qhWLskJcqgZV4FJ1Wi/eW5JT4lIVC+LYosDX5by7A0tVdY+qHgAWAOdHOqGcm1Qcuz75petbXvO8uT61bVne9SkSgS7bKJyvIpeBP45aod4OALlbdx6kS1UaM99dHvE7RIc3e7xEtMhbBQwSkSPcJb3PAjqUTRTqJrXL3KQMIyruenw2A9M6s+DZMQxM71yxS1XnNsxf+mXMrlk8oyBePQr8tMhbA9wPvAO8DawECitIV+Im1aysm1Qcuz75petbXlt6c33KzSvv+hSJQJdtFM5XkcvAH0et0NodQNsWjSt2qbrzOU4e9TBTnpwLVOBStTDcpSrR8dXMWFWnqmqmqg4GtgNfRUpfl92BcX3yS9evvKZ3d12fch3d19/NYtjgnuV0i12fZoW4PkUiaGV7sM5XkcvAH0et5Ws20aV983CXqo/CX19W6VJVxiA5VsRzTc3XIR0i0lJV80SkI05/Wv/I6f1x+wmSmxT4Vwb3j72Ii1zXp8vP6c+xndtw35NvkRbi+nT9pOfpfcFkmjSqx9NTri65N2nnTuTn/F/Yv/8AcxZ8wauP3sCxndsEr2wP0vkKoNfI0jJ4a8EXzAwtAx8ctQoLixj38GvM/Pu1JCdLqUvVb3/FypzNpS5V152FKo5L1UMVuVSt8/gv1jvxPKTDbzepRcARwH5gjKrOj5Q+M7O3Ll4a0UXPOEhs6SEHP5/3WNNs4NiYa+5dPZ2i/O+rddPSM3vrgsWfVp0QaFw3OeHcpAb5qW8YxqHHlh4yDCPhiOfmp68vCgzDSExi9aJARM4UkS9FZK2I3FHB8Toi8n/u8aUiclRVmhbUDMOImljMKBCRZOAJYBjQA7hMRHqUSXYNsF1Vjwb+jjNMLCIW1AzDiJ7YzJPqC6xV1XWqug94CRhZJs1I4Dn371eBIVLFGBsLaoZhRIVArKZJtQM2hXze7O6rMI073XInzoiKSomrFwXLl2dtq1tLNnpI2hzY5kMWTDdYeQ2abjzk9cjqXmz58qx5dWtJc4/JU0UkdJzWU6r6VHXzEIm4Cmqq2sJLOhH5zI+xL6YbrLwGTTdIeY2Eqp4ZI6kthM8Hb+/uqyjNZhFJARoDP0YSteanYRg1xTKgq4h0EpHawKXArDJpZgFXuX9fCLyvVYygjquammEYhw+qekBERgPzgGTgGVVdLSJ34ywuOQuYCkwTkbXATziBLyJBDWp+tclNN1h5DZpukPJ6SFDVOcCcMvsmhPz9C3BRNJq+zv00DMM41FifmmEYCUXgglpV0yoOUvMZEckTkVWx0HM1O4jIByKSLSKrReTmGOmmisinIvK5qzs5Froh+skiskJE3oyh5gYR+UJEVpZ5vV8dzSYi8qqI5IjIGhEZEAPNbm4ei7ddInJLjPJ7q3u/VonIDBFJjZHuza7m6ljlNfAcaqeX6mw4nYnfAJ2B2sDnQI8Y6A4GMoBVMcxrGyDD/bshzgKZscirAA3cv2sBS4H+Mcz3GOBF4M0Yam4Amsf4WXgO+K37d22giQ/P2vfAkTHQagesB+q6n18GRsVA93icZfPr4fSPvwccHctyCOIWtJqal2kVUaOqC3HerMQMVf1OVZe7f/8MrKH8aOmD0VVV3e1+rOVuMekYFZH2wNnA07HQ8wsRaYzzQzQVQFX3qeqOyGdFzRDgG1X1MhjcCylAXXesVT0gNwaaUZsbHQ4ELah5mVYRd7grC6Tj1KpioZcsIiuBPOBdVY2JLvAIMA6I9YL2CrwjIlkicm0M9DoBW4F/u03lp0UkspFA9FwKzIiFkKpuAf4GfAt8B+xU1XdiIO3J3OhwI2hBLXCISANgJo6Zc0zsslS1UFXTcEZg93U9VquFiAwH8lQ1q9oZLM9JqpqBsxrDjSIyuJp6KTjdBf9S1XQgH4hJ/yqAOxB0BPBKjPSa4rQoOgFtgfoicmV1ddWjudHhRtCCmpdpFXGDiNTCCWjTVfW1WOu7Ta4PgFhMWxkIjBCRDTjN+tNE5IUY6BbXVFDVPOB1nG6E6rAZ2BxSQ30VJ8jFimHAclX9IUZ6pwPrVXWrqu4HXgNOjIWwRmludDgQtKDmZVpFXOAujzIVWKOqD8dQt4WINHH/rgsMBXKqq6uq41W1vaoehVOu76tqtWsTIlJfRBoW/w2cgdNsqk5evwc2iUg3d9cQILtaGQ3nMmLU9HT5FugvIvXc52IITh9rtRGRlu7/i82NXoyFbpAJ1IwCrWRaRXV1RWQGcArQXEQ2AxNVdWo1ZQcCvwa+cPu/AO5UZwR1dWgDPOcusJcEvKyqMRt+4QOtgNfdJbBSgBdV9e0Y6P4BmO7+uK0Drq4ivSfcwDsU+H0s9ABUdamIvAosBw4AK4jdLICZIlJsbnSjDy9MAofNKDAMI6EIWvPTMAwjIhbUDMNIKCyoGYaRUFhQMwwjobCgZhhGQmFBLUCISKG7esQqEXnFnRpzsFrPisiF7t9PV+C3GJr2FBGJerCouzpHOYOOyvaXSbM70vEK0k8SkbHR5tFIPCyoBYsCVU1T1eOBfcB1oQfdydJRo6q/VdVIg1dPIUYj4A3DbyyoBZdFwNFuLWqRiMwCst3J7g+KyDIR+a+I/B6cGQ4i8ri7Ft17QMtiIRH5UER6u3+fKSLL3fXa5ruT8a8DbnVriYPcWQ0z3WssE5GB7rlHiMg77tpeT+PBzlZE/uNOdF9ddrK7iPzd3T9fRFq4+7qIyNvuOYtE5NhYFKaROARqRoHh4NbIhuFMYgZn3uPxqrreDQw7VbWPiNQBFovIOzirhHQDeuCM8s8Gnimj2wL4X2Cwq9VMVX8Skf8Bdqvq39x0LwJ/V9WP3Ok583CWwZkIfKSqd4vI2cA1Hr7O/3OvURdYJiIzVfVHoD6O+catIjLB1R6NMxL/OlX9WkT6Af8ETjuIYjQSFAtqwaJuyJSrRThzS08EPlXV9e7+M4ATivvLcHwSu+KsPzZDVQuBXBF5vwL9/sDCYi1VrWyNudOBHlLqwN3IXY1kMO56Xqr6lohs9/CdbhKR89y/O7h5/RFn+aP/c/e/ALzmXuNE4JWQa9fxcA3jMMKCWrAocJccKsH9x50fugv4g6rOK5PurBjmIwlntd1fKsiLZ0TkFJwAOUBV94jIh0Bly1yre90dZcvAMEKxPrXEYx5wvbvsESJyjDtJeyFwidvn1gY4tYJzPwEGi0gn99xm7v6fcZYkL+YdnAnluOmKg8xC4HJ33zCgaRV53U/uswAAAMpJREFUbQxsdwPasTg1xWKScMxrcTU/ctejWy8iF7nXEBHpVcU1jMMMC2qJx9M4/WXLxTGSeRKnRv468LV77HlgSdkTVXUrcC1OU+9zSpt/s4Hzil8UADcBvd0XEdmUvoWdjBMUV+M0Q7+tIq9vAykisgb4K05QLSYfZwHMVTh9Zne7+68ArnHzt5oYLOduJBa2SodhGAmF1dQMw0goLKgZhpFQWFAzDCOhsKBmGEZCYUHNMIyEwoKaYRgJhQU1wzASCgtqhmEkFP8fULUP/Mr+nnkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "classify(tr_images, tr_labels, ts_images, ts_labels, \"Without RBM\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
